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General existence principles for nonlocal boundary value problems with \(\phi\)-Laplacian and their applications. (English) Zbl 1147.34007
The paper gives general existence principles that can be applied for a large class of nonlocal boundary value problems of \(\phi\)-Laplacian type, namely
\[ (\phi(x'))' = f_1(t,x,x') + f_2(t,x,x')F_1x + f_3(t,x,x')F_2x, \]
\[ \alpha(x)= 0=\beta(x), \] where the functions \(f_j\) satisfy local Carathéodory conditions, and may have singularities in their phase variables, \(F_i:C^1[0,T]\to C^0[0,T]\) and \(\alpha,\beta:C^1[0,T]\to \mathbb R\) are continuous. Proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications and an example are given for some singular boundary value problems.

34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
Full Text: DOI
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